As a response to never ending high bandwidth demands, the IEEE has ratified its 40/100 Gb/s Ethernet Standard IEEE 802.3ba in June 2010. The deployment of 100 Gb/s Ethernet (GbE) has already started and it is expected to accelerate in next few years. At these ultra-high data rates, the performance of fiber-optic communication systems is degraded significantly due to presence of various linear and nonlinear impairments. To deal with those channel impairments novel advanced techniques in modulation and detection, coding and signal processing have been intensively studied. For carrier phase estimation (CPE), the algorithmic DSP-based approaches are highly popular, and can be categorized into two broad categories data-aided and non-data-aided. The MAP and ML approaches are particularly efficient in CPE; however, the complexity of such algorithms grows exponentially with the channel memory. Even upon compensation of chromatic dispersion and nonlinearity phase compensation there will be some residual phase error. It has been experimentally verified that even in beyond 100 Gb/s transmission the distribution of samples upon compensation of linear and nonlinear impairments is still Gaussian-like with the residual phase error that can properly be modeled as a Markov process.